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Three perpendicular inverse theorem

Lecture



Theorem .

If the straight line on the plane is perpendicular to the oblique, then it is also perpendicular to the projection of the oblique.

Three perpendicular inverse theorem

Proof .

Similar to the three perpendiculars theorem, if a straight line with perpendicular to inclined CA, then, being perpendicular to and straight line CA`, is perpendicular to the plane β, and hence to the projection of inclined BC. The theorem is proved.
created: 2014-10-05
updated: 2026-03-09
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Lectures and tutorial on "Stereometry"

Terms: Stereometry

Stereometry
Stereometry
Axioms of stereometry
Plane and point
Plane and straight
Parallel lines in space
Parallel straight lines in space. Properties
Sign of parallel lines in space
Sign of parallelism of a line and a plane
Sign of parallel planes
The existence of a plane parallel to the plane
Properties of parallel planes
Perpendicular lines in space
The sign of perpendicularity of the line and the plane
Property perpendicular line and plane
Property of lines perpendicular to the plane
Perpendicular and inclined
Three perpendicular theorem
Three perpendicular inverse theorem
Perpendicular planes
The sign of perpendicular planes
The distance between intersecting straight
The distance between intersecting straight lines. Properties
Cartesian coordinates in space
The distance between points in space
The coordinates of the middle of the segment in space
Movement in space
Parallel transport in space
Similarity of spatial figures
Homothety in space
Angle between intersecting straight lines
Angle between a straight line and a plane - definition, examples of finding.
The angle between two intersecting planes - definition, examples of finding.
The coordinates of the point of intersection of two straight lines are examples of finding.
The coordinates of the point of intersection of a line and a plane are examples of finding.
The area of ​​the orthogonal projection of the polygon
Vectors in space
Actions on vectors
Dihedral angle
Triangular and multifaceted corners
Polyhedra
Prism
Straight prism
Straight prism. Properties
Parallelepiped
Parallelepiped. Properties
Central symmetry of the parallelepiped
Rectangular parallelepiped
Rectangular parallelepiped. Property
Pyramid
Truncated pyramid
Correct pyramid
The correct pyramid. Properties
Regular polyhedra
Body rotation. Cylinder
Cylinder. Properties
Cylinder section plane
Prism inscribed and described
Cone
The cross section of the cone planes
Pyramid inscribed and described
Ball
The cross section of the ball plane
Ball symmetry
Tangent plane to the ball
Intersection of two spheres
Polyhedra inscribed and described
Volumes of polyhedra. Volume
Equal body
Volume of a rectangular parallelepiped
Inclined parallelepiped volume
Arbitrary prism volume
Triangular prism volume
Volume of a triangular pyramid
The volume of an arbitrary pyramid
The volume of the truncated pyramid
Volumetric and surfaces of bodies of revolution. Cylinder
Cone volume
Truncated cone volume
General formula for volumes of bodies of revolution
Ball volume
Ball segment volume
Volume of the ball sector
The surface area of ​​the cylinder
Cone side surface area
Sphere area